A set of cars
A set of blue cars
A key concept in the field of pattern recognition is that of uncertainty. It arises both through noise on measurements, as well as through the finite size of data sets. Hence, measurements will never be perfect. Objects within a class will vary.
Probability theory provides a consistent framework for the quantification and manipulation of uncertainty and forms one of the central foundations for pattern recognition.
Probability theory is nothing but common sense reduced to calculation. — Pierre Laplace, 1812
Scientists from all over the world use the same language to talk about collections of objects. This language is known as Set Theory.
A set is simply a collection of objects. For example:
A set of cars
A set of blue cars
The members of a set are called elements. So, a blue car is an element of the set of all cars. Written down in the notation of the set theory, it would look like this:
Another example is that you are an element of the set of all people in the world.
More abstractly written down, look at the following set $A$, with distinct elements $a_1$ till $a_5$:
$A=\{a_1,a_2,...,a_5\}$
As you can see, sets are denoted by capital letters ($A, B, C...$), and the elements of the set are written between curly brackets. If you want to denote that $a_1$ is an element of $A$, and that $a_6$ is not an element of $A$, you write it like this:
$a_1 \in A,\space a_6 \not \in A$
We can represent the previous set as the following:
Sets are drawn as ellipses. Such drawing is known as Venn diagram.